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Vanishing John–Nirenberg spaces

  • Jin Tao , Dachun Yang ORCID logo EMAIL logo and Wen Yuan
Published/Copyright: February 5, 2021

Abstract

There still exist many unsolved problems on the study related to John–Nirenberg spaces. In this article, the authors introduce two new vanishing subspaces of the John–Nirenberg space JN p ( n ) denoted, respectively, by VJN p ( n ) and CJN p ( n ) , and establish their equivalent characterizations which are counterparts of those characterizations for the classic spaces VMO ( n ) and CMO ( n ) obtained, respectively, by D. Sarason and A. Uchiyama. All these results shed some light on the mysterious space JN p ( n ) . The approach strongly depends on the fine geometrical properties of dyadic cubes, which enable the authors to subtly classify any collection of interior pairwise disjoint cubes.

MSC 2010: 42B35; 42B30; 46E35

Communicated by José María Martell


Award Identifier / Grant number: 11971058

Award Identifier / Grant number: 12071431

Award Identifier / Grant number: 11871100

Award Identifier / Grant number: 2020YFA0712900

Funding statement: This project is supported by the National Natural Science Foundation of China by Grant Nos. 11971058, 12071431 and 11871100, and also by the National Key Research and Development Program of China by Grant No. 2020YFA0712900.

Acknowledgements

Jin Tao would like to thank Yangyang Zhang and Hongchao Jia for some useful discussions on Lemma 4.2, Remark 5.9, and Proposition 5.7. The authors would also like to thank the referee for her/his carefully reading and several motivating remarks which indeed improve the quality of this article.

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Received: 2020-06-10
Revised: 2020-09-15
Accepted: 2021-01-21
Published Online: 2021-02-05
Published in Print: 2022-10-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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